Ondřej Čadek

Inferences of viscosity from the oceanic geoid: Indication of a low viscosity zone below the 660-km discontinuity

Abstract We have attempted to infer details of the viscosity structure in the top 1000 km of the mantle from the geoid and tomographic structure beneath the oceans. In order to eliminate the gravity signal from problematic masses located below the subduction zones and the continents, we have considered only the intermediate degrees of the oceanic geoid (l = 12–25). A genetic algorithm has been used to determine the family of viscosity models which give the best correlation with the observed geoid. Our inversion clearly identifies the asthenosphere just below the lithosphere and also confirms the viscosity increase in the lower mantle predicted by previous inferences, but suggests that the main viscosity jump occurs at a depth of about 1000 km and not at the usually stated 660-km boundary. Somewhere in the depth range of 400–1000 km, a low viscosity zone may exist where the viscosity decreases to a value comparable with the asthenosphere. Existence of such a low viscosity zone is supported by recent analysis of deep mantle anisotropy which favours a flow pattern with a strong horizontal component in the top part of the lower mantle. Unfortunately, the resolution of the inversion as well as the quality of recent seismic tomographic models are not sufficient to localize the depth and to come up with a higher accuracy for the viscosity of this low viscosity channel.

A global geoid model with imposed plate velocities and partial layering

Most inversions of the long-wavelength geoid in conjunction with the seismic tomographic information have so far been carried out under the assumption of either purely whole mantle or perfectly layered circulation. Moreover, modeling the lithosphere as a spherical shell with a uniform low viscosity was found to yield the best fit to the observed geoid. We have tested whether a good prediction of the geoid can also be achieved by including two constraints: a semipermeable behavior of the 660-km discontinuity and surface plate velocities equal to the observed ones. The mass transfer between upper and lower mantle has been changed by imposing a surface density anomaly at a depth of 660 km, which is proportional to the mass anomaly needed to achieve perfectly layered circulation. On the top of the mantle we assume a stiff lithosphere that moves with a velocity corresponding to the observed plate motion. The viscosity only varies with depth. Considering a simple three-layer viscosity structure and changing the permeability of the 660-km interface, we have obtained a satisfactory variance reduction of the geoid data (∼75% for degrees 2–12). The best fit to the geoid is obtained if the mass transfer across the 660-km boundary is reduced to one third in comparison with the purely whole mantle model. The best fitting viscosity profile is characterized by a clearly defined asthenosphere and a viscosity increase by at least 2 orders of magnitude in the lower mantle. The amplitudes of dynamic topography predicted by our model are remarkably small (∼100 m), thus fully compatible with the observation.

Geophysical inferences of thermal‐chemical structures in the lower mantle

Lateral variations of the temperature field in the lower mantle have been reconstructed using new results in mineral physics and seismic tomographic data. We show that, with the application of high-pressure experimental values of thermal expansivity and of sound velocities, the slow seismic anomalies in the lower mantle under the Pacific and Africa can be converted into realistically looking plume structures with large dimensions of 0(10³ km). The outer fringes of the plumes have an excess temperature of around 400 K. In the core of the plumes are found tongue-like structures with extremely high thermal anomalies. These values can exceed 1200 K and are too high to be explained on the basis of thermal anomalies alone. We suggest that these major plumes in the deep mantle may be driven by both thermal and chemical buoyancies or that enhanced conductive heat-transfer may be important there.

Modeling the dynamic component of the geoid and topography of Venus

[1] We analyze the Venusian geoid and topography to determine the relative importance of isostatic, elastic and dynamic compensation mechanisms over different degree ranges. The geoid power spectrum plotted on a log-log scale shows a significant change in its slope at about degree 40, suggesting a transition from a predominantly dynamic compensation mechanism at lower degrees to an isostatic and/or elastic mechanism at higher degrees. We focus on the dynamic compensation in the lower-degree interval. We assume that (1) the flow is whole mantle in style, (2) the long-wavelength geoid and topography are of purely dynamic origin, and (3) the density structure of Venus’ mantle can be approximated by a model in which the mass anomaly distribution does not vary with depth. Solving the inverse problem for viscosity within the framework of internal loading theory, we determine the families of viscosity models that are consistent with the observed geoid and topography between degrees 2 and 40. We find that a good fit to the data can be obtained not only for an isoviscous mantle without a pronounced lithosphere, as suggested in some previous studies, but also for models with a high-viscosity lithosphere and a gradual increase in viscosity with depth in the mantle. The overall viscosity increase across the mantle found for the latter group of models is only partially resolved, but profiles with a � 100-km-thick lithosphere and a viscosity increasing with depth by a factor of 10‐80, hence similar to viscosity profiles expected in the Earth’s mantle, are among the best fitting models.

Coupling mantle convection and tidal dissipation: Applications to Enceladus and Earth‐like planets

[1] Anelastic dissipation of tidal forces likely contributes to the thermal budget of several satellites of giant planets and Earth‐like planets closely orbiting other stars. In order to address how tidal heating influences the thermal evolution of such bodies, we describe here a new numerical tool that solves simultaneously mantle convection and tidal dissipation in a three‐dimensional spherical geometry. Since the two processes occur at different timescales, tidal dissipation averaged over a forcing period is included as a volumetric heat source for mantle dynamics. For the long‐term flow, a purely viscous material is considered, whereas a Maxwell‐like formalism is employed for the tidal viscoelastic problem. Due to the strongly temperature dependent rheological properties of both mechanisms, the coupling is achieved via the temperature field. The model is applied to two examples: Enceladus and an Earth‐like planet. For Enceladus, our new 3‐D method shows that the tidal strain rates are strongly enhanced in hot upwellings when compared with classical methods. Moreover, the heat flux at the base of Enceladus’ ice shell is strongly reduced at the poles, thus favoring the preservation of a liquid reservoir at depth. For Earth‐like planets, tidal dissipation patterns are predicted for different orbital configuration. Thermal runaway is observed for orbital periods smaller than a critical value (e.g., 30 days for an eccentricity of 0.2 and 3:2 resonance). This is likely to promote large‐scale melting of the mantle and Io‐like volcanism.

Toroidal/poloidal energy partitioning and global lithospheric rotation during Cenozoic time

The motion of surficial plates can be split into two terms: the toroidal field related to shear between plates or to spin around their centres and the poloidal field associated with horizontal divergence at ridges and subductions. Recent papers have suggested that the present-day plate motion minimizes the ratio of toroidal to poloidal energies [1] and that the existence of a global lithospheric rotation results from viscosity variations between oceans and continents [2]. This paper tests and confirms these two hypotheses using plate reconstructions during Cenozoic time. The partition of energy between the two modes always favours the poloidal velocities. The global rotation computed using a viscosity one order of magnitude lower below oceans than below continents agrees with observations. The existence of a non-linear rheology in a uniform asthenosphere leads to a satisfactory location of the global lithospheric rotation but with too small an amplitude.

Lower mantle thermal structure deduced from seismic tomography, mineral physics and numerical modelling

Abstract The long-wavelength thermal anomalies in the lower mantle have been mapped out using several seismic tomographic models in conjunction with thermodynamic parameters derived from high-pressure mineral physics experiments. These parameters are the depth variations of thermal expansivity and of the proportionality factor between changes in density and seismic velocity. The giant plume-like structures in the lower mantle under the Pacific Ocean and Africa have outer fringes with thermal anomalies around 300–400 K, but very high temperatures are found in the center of the plumes near the base of the core-mantle boundary. These extreme values can exceed +1500 K and may reflect large hot thermal anomalies in the lower mantle, which are supported by recent measurements of high melting temperatures of perovskite and iron. Extremely cold anomalies, around −1500 K, are found for anomalies in the deep mantle around the Pacific rim and under South America. Numerical simulations show that large negative thermal anomalies of this magnitude can be produced in the lower mantle, following a catastrophic flushing event. Cold anomalies in the mid-lower mantle have modest magnitudes of around −500 K. A correlation pattern exists between the present-day locations of cold masses in the lower mantle and the sites of past subduction since the Cretaceous. Results from correlation analysis show that the slab mass-flux in the lower mantle did not conform to a steady-state nature but exhibited time-dependent behavior.

MANTLE VISCOSITY DERIVED BY GENETIC ALGORITHM USING OCEANIC GEOID AND SEISMIC TOMOGRAPHY FOR WHOLE-MANTLE VERSUS BLOCKED-FLOW SITUATIONS

Abstract We have applied the genetic algorithm (GA) technique, a nonlinear global optimization method, to determine the radial viscosity structure of the mantle from regional geoidal patterns. From numerical simulations of 2-D mantle convection, we examine the horizontal spectra of the vertical mass flux at 660 km depth and find that for long wavelengths there are minor differences between partially layered convection induced by the phase transitions and mantle convection without any phase transition. The differences in the spectra of the vertical mass flux become more prominent at shorter wavelengths. This result has led us to study mantle viscosity for the intermediate wavelength geoid from the whole-mantle and blocked-flow situations, in which the appropriate boundary condition is imposed on the radial velocity at 660 km depth. In order to confirm the robustness of this study, two different density models have been used, which were constructed from three tomographic models and appropriate velocity-to-density scaling relations based on recent results from mineral physics. We have analyzed only oceanic geoid spanning between spherical harmonic degree l=12–25. The correlation of the predicted geoid with the observations over the Atlantic, Indian, and Pacific Oceans have been employed as the fitting function in our GA approach, which has been modified from the common algorithm. In constructing the families of suitable viscosity profiles, we have used 100 parents, which have been iterated for 100 generations, and have been started with 10 different sets of initial parents. Convergence to acceptable viscosity solutions is obtained for all the three oceans and for both the whole-mantle and layered models. In some cases multiple viscosity solutions are found acceptable by using the correlation criteria. The outstanding feature of these models is the nearly ubiquitous presence of two low viscosity zones, one lying under the lithosphere, the other right under the bottom of the spinel to perovskite phase change. The solutions for the whole-mantle model can fit better and are preferred over the solutions with the layered boundary condition, which generally result in unrealistic viscosity profiles. Our results would suggest a more complex mantle viscosity structure, which has not been detected previously from geoid signals with longer wavelengths, and also reveal the potential difficulties in treating the dynamical boundary condition at the 660 km discontinuity.

Can long‐wavelength dynamical signatures be compatible with layered mantle convection?

Analyses of the long-wavelength geoid with seismic tomographic models have been providing for a long time important estimates of mantle viscosity. These estimates have nearly been derived under the assumption of whole mantle flow. It has been commonly held that a fully impermeable boundary at 660 km depth is incompatible with the long-wavelength gravity signal. On the other hand, models with whole mantle circulation, which can explain a large portion of the geoid signal, usually produce excessive amplitudes of the dynamical topography, especially for long wavelengths. Using recent tomographic models together with genetic algorithm we have successfully demonstrated that the layered convection model can also produce a reasonable fit to the geoid, which is comparable in quality with that obtained for the whole mantle model. The layered model can simultaneously yield realistic amplitudes of the dynamical topographies of the surface and the 660-km discontinuity.

Tidally induced thermal runaways on extrasolar earths : impact on habitability

We study the susceptibility of extrasolar Earth-like planets to tidal dissipation by varying orbital, rheological, and heat transfer parameters. We employ a three-dimensional numerical method solving the coupled problem of mantle convection and tidal dissipation. A reference model mimicking a plate tectonic regime and reproducing Earths present-day heat output is considered. Four other models representing less efficient heat transfer regimes are also investigated. For these five initial models, we determine the orbital configurations under which a positive feedback between tidal dissipation and temperature evolution leads to a thermal runaway. In order to describe the occurrence of thermal runaways, we develop a scaling that relates the global dissipated power to a characteristic temperature and to the orbital parameters. For all numerical experiments sharing the same initial temperature conditions, we show that the reciprocal value of the runaway timescale depends linearly on the global dissipated power at the beginning of the simulation. In the plate tectonic-like regime, Earth-like planets in the habitable zone (HZ) of 0.1 M ☉ stars experience thermal runaways for 1:1 spin-orbit resonance if the eccentricity is sufficiently high (e>0.02 at a 4 day period, e>0.2 at a 10 day period). For less efficient convective regimes, runaways are obtained for eccentricities as low as ~0.004 at the inner limit of the HZ. In the case of 3:2 spin-orbit resonance, the occurrence of thermal runaways is independent of eccentricity and is predicted for orbital periods lower than 12 days. For less efficient convective regimes, runaways may occur at larger orbital periods potentially affecting the HZ of stars with a mass up to 0.4 M ☉. Whatever the convective regime and spin-orbit resonance, tidal heating within Earth-like planets orbiting in the HZ of stars more massive than 0.5 M ☉ is not significant.